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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/vector_fe/vector_fe_ex4" target="_blank">Open vector_fe_ex4 in new tab.</a>
<a name="output"></a> 
<br><br><br> <h1> The console output of the program: </h1> 
<pre>
***************************************************************
* Running Example vector_fe_ex4:
*   example-opt element_type=HEX20 -pc_type jacobi 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={3}
  spatial_dimension()=3
  n_nodes()=425
    n_local_nodes()=425
  n_elem()=64
    n_local_elem()=64
    n_active_elem()=64
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u" 
    Finite Element Types="NEDELEC_ONE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" 
    n_dofs()=300
    n_local_dofs()=300
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 23.4
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 33
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 10.5823
Linear solve starting, tolerance 1e-12
Linear solve finished, step 8, residual 1.77336e-12
Trying full Newton step
  Current Residual: 0.00343459
  Nonlinear step: |du|/|u| = 1, |du| = 3.91397
Assembling the System
Nonlinear Residual: 0.00343459
Linear solve starting, tolerance 1e-12
Linear solve finished, step 64, residual 1.72119e-24
Trying full Newton step
  Current Residual: 6.84753e-15
  Nonlinear solver converged, step 1, residual reduction 6.47071e-16 < 1e-06
  Nonlinear solver converged, step 1, relative step size 6.67306e-12 < 1e-06
WARNING: Shape function gradients for HCurl elements are not currently being computed!./include/libmesh/hcurl_fe_transformation.h, line 71, compiled Apr 12 2016 at 11:07:08 ***
WARNING: Shape function Hessians for HCurl elements are not currently being computed!./include/libmesh/hcurl_fe_transformation.h, line 90, compiled Apr 12 2016 at 11:07:08 ***
WARNING: Shape function divergences for HCurl elements are not currently being computed!./include/libmesh/hcurl_fe_transformation.h, line 117, compiled Apr 12 2016 at 11:07:08 ***
L2-Error is: 0.172154
HCurl semi-norm error is: 1.47497
HCurl-Error is: 1.48498

 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 10:35:36 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.036559, Active time=0.024773                                                  |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     1          0.0000      0.000036    0.0000      0.000036    0.15     0.15     |
|   build_sparsity()                 1          0.0003      0.000289    0.0003      0.000319    1.17     1.29     |
|   create_dof_constraints()         1          0.0000      0.000010    0.0000      0.000010    0.04     0.04     |
|   distribute_dofs()                1          0.0001      0.000058    0.0002      0.000237    0.23     0.96     |
|   dof_indices()                    704        0.0003      0.000000    0.0003      0.000000    1.08     1.08     |
|   prepare_send_list()              2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         1          0.0002      0.000179    0.0002      0.000179    0.72     0.72     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          1          0.0017      0.001678    0.0051      0.005091    6.77     20.55    |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               1          0.0013      0.001342    0.0013      0.001342    5.42     5.42     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        453        0.0013      0.000003    0.0013      0.000003    5.40     5.40     |
|   init_shape_functions()           453        0.0004      0.000001    0.0004      0.000001    1.63     1.63     |
|                                                                                                                 |
| FEMSystem                                                                                                       |
|   assembly()                       2          0.0053      0.002657    0.0099      0.004957    21.45    40.02    |
|   assembly(get_residual)           2          0.0016      0.000802    0.0061      0.003027    6.47     24.44    |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             768        0.0021      0.000003    0.0021      0.000003    8.39     8.39     |
|   compute_face_map()               384        0.0005      0.000001    0.0005      0.000001    1.82     1.82     |
|   init_face_shape_functions()      384        0.0009      0.000002    0.0009      0.000002    3.71     3.71     |
|   init_reference_to_physical_map() 453        0.0072      0.000016    0.0072      0.000016    29.07    29.07    |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 1          0.0002      0.000194    0.0002      0.000194    0.78     0.78     |
|   renumber_nodes_and_elem()        2          0.0000      0.000018    0.0000      0.000018    0.15     0.15     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         1          0.0000      0.000014    0.0064      0.006448    0.06     26.03    |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0001      0.000146    0.0001      0.000146    0.59     0.59     |
|                                                                                                                 |
| NewtonSolver                                                                                                    |
|   solve()                          1          0.0002      0.000223    0.0172      0.017170    0.90     69.31    |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               1          0.0000      0.000012    0.0000      0.000012    0.05     0.05     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          2          0.0010      0.000489    0.0010      0.000489    3.95     3.95     |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            3622       0.0248                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example vector_fe_ex4:
*   example-opt element_type=HEX20 -pc_type jacobi 
***************************************************************
***************************************************************
* Running Example vector_fe_ex4:
*   example-opt element_type=HEX27 -pc_type jacobi 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={3}
  spatial_dimension()=3
  n_nodes()=729
    n_local_nodes()=729
  n_elem()=64
    n_local_elem()=64
    n_active_elem()=64
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u" 
    Finite Element Types="NEDELEC_ONE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="FIRST", "THIRD" 
    n_dofs()=300
    n_local_dofs()=300
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 23.4
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 33
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 10.5823
Linear solve starting, tolerance 1e-12
Linear solve finished, step 8, residual 1.77359e-12
Trying full Newton step
  Current Residual: 0.00343562
  Nonlinear step: |du|/|u| = 1, |du| = 3.91397
Assembling the System
Nonlinear Residual: 0.00343562
Linear solve starting, tolerance 1e-12
Linear solve finished, step 60, residual 1.26751e-24
Trying full Newton step
  Current Residual: 6.37431e-15
  Nonlinear solver converged, step 1, residual reduction 6.02353e-16 < 1e-06
  Nonlinear solver converged, step 1, relative step size 6.6735e-12 < 1e-06
WARNING: Shape function gradients for HCurl elements are not currently being computed!./include/libmesh/hcurl_fe_transformation.h, line 71, compiled Apr 12 2016 at 11:07:08 ***
WARNING: Shape function Hessians for HCurl elements are not currently being computed!./include/libmesh/hcurl_fe_transformation.h, line 90, compiled Apr 12 2016 at 11:07:08 ***
WARNING: Shape function divergences for HCurl elements are not currently being computed!./include/libmesh/hcurl_fe_transformation.h, line 117, compiled Apr 12 2016 at 11:07:08 ***
L2-Error is: 0.172154
HCurl semi-norm error is: 1.47497
HCurl-Error is: 1.48498

 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 10:35:36 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.045556, Active time=0.038749                                                  |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     1          0.0000      0.000042    0.0000      0.000042    0.11     0.11     |
|   build_sparsity()                 1          0.0002      0.000249    0.0003      0.000287    0.64     0.74     |
|   create_dof_constraints()         1          0.0000      0.000013    0.0000      0.000013    0.03     0.03     |
|   distribute_dofs()                1          0.0001      0.000076    0.0003      0.000341    0.20     0.88     |
|   dof_indices()                    704        0.0003      0.000000    0.0003      0.000000    0.79     0.79     |
|   prepare_send_list()              2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         1          0.0003      0.000265    0.0003      0.000265    0.68     0.68     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          1          0.0019      0.001916    0.0099      0.009904    4.94     25.56    |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               1          0.0013      0.001339    0.0013      0.001339    3.46     3.46     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        453        0.0014      0.000003    0.0014      0.000003    3.54     3.54     |
|   init_shape_functions()           453        0.0004      0.000001    0.0004      0.000001    1.00     1.00     |
|                                                                                                                 |
| FEMSystem                                                                                                       |
|   assembly()                       2          0.0051      0.002556    0.0144      0.007220    13.19    37.27    |
|   assembly(get_residual)           2          0.0016      0.000786    0.0108      0.005387    4.06     27.81    |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             768        0.0024      0.000003    0.0024      0.000003    6.30     6.30     |
|   compute_face_map()               384        0.0005      0.000001    0.0005      0.000001    1.21     1.21     |
|   init_face_shape_functions()      384        0.0019      0.000005    0.0019      0.000005    4.77     4.77     |
|   init_reference_to_physical_map() 453        0.0200      0.000044    0.0200      0.000044    51.51    51.51    |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 1          0.0002      0.000179    0.0002      0.000179    0.46     0.46     |
|   renumber_nodes_and_elem()        2          0.0000      0.000007    0.0000      0.000007    0.04     0.04     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         1          0.0000      0.000013    0.0113      0.011256    0.03     29.05    |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0001      0.000143    0.0001      0.000143    0.37     0.37     |
|                                                                                                                 |
| NewtonSolver                                                                                                    |
|   solve()                          1          0.0002      0.000185    0.0262      0.026231    0.48     67.69    |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               1          0.0000      0.000015    0.0000      0.000015    0.04     0.04     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          2          0.0008      0.000414    0.0008      0.000414    2.14     2.14     |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            3622       0.0387                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example vector_fe_ex4:
*   example-opt element_type=HEX27 -pc_type jacobi 
***************************************************************
</pre>
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